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* Reaction-Diffusion Model * Reaction-Diffusion Model
Reaction-Diffusion system simulation using the Gray-Scott model, in [[https://www.dyalog.com/][Dyalog APL]]. [[https://en.wikipedia.org/wiki/Reaction%E2%80%93diffusion_system][Reaction-Diffusion system]] simulation using the Gray-Scott model, in [[https://www.dyalog.com/][Dyalog APL]].
[[img.png]] [[img.png]]
** Running
[[https://www.dyalog.com/download-zone.htm][Install Dyalog APL]] and [[https://en.wikipedia.org/wiki/Netpbm][Netpbm]] (~apt-get install netpbm~). Then run
~make~. This will create the =img.pnm= and =img.png= files in the
current directory.
The images are generated from APL by creating a [[https://en.wikipedia.org/wiki/Netpbm][Netpbm]] file, which are
nice because they are just plain-text. It is then converted to PNG
using ~pnmtopng~.
** Parameters
All the parameters are defined directly in [[grayscott.dyalog]].
The parameters of the model are:
- ~dt~: the time step,
- ~da~: the diffusion rate for A,
- ~db~: the diffusion rate for B,
- ~f~: the feed rate for A,
- ~k~: the kill rate for B.
Additionally, you can change ~N~, the size of the grid, and ~steps~,
the number of time steps to simulate.
Finally, the function ~mat2pbm~ exports to a bitmap (black and white)
format, while ~mat2pgm~ exports a grayscale image.
** References
[[http://www.karlsims.com/rd.html][This page]] gives a good explanation of the Gray-Scott model. [[https://github.com/loftytopping/Env_modelling/blob/master/Spatio-temporal-modelling/Reaction_diffusion_2D.ipynb][This
notebook]] [[https://colab.research.google.com/github/loftytopping/Env_modelling/blob/master/Spatio-temporal-modelling/Reaction_diffusion_2D.ipynb][(Colab)]] gives a nice example of implementation in Python with
Numpy. For even more details on the model and a classification of
pattern, see [[http://mrob.com/pub/comp/xmorphia/][this page]].